A widely used technique for searching for oil or gas is the seismic exploration of subsurface geophysical structures. The seismic exploration process consists of generating seismic waves (i.e., sound waves) directed toward the subsurface area, gathering data on reflections of the generated seismic waves at interfaces between layers of the subsurface, and analyzing the data to generate a profile (image) of the geophysical structure, i.e., the layers of the investigated subsurface. This type of seismic exploration can be used both on the subsurface of land areas and for exploring the subsurface of the ocean floor.
It is known by those of ordinary skill in the art of seismic exploration that an appropriate choice of frequencies to drive a sound producing device can be used to generate seismic waves whose reflections can, in turn, be used to determine the possible or probable location of hydrocarbon deposits under, e.g., the ocean floor. The sound producing device in such marine applications can be referred to as a marine vibrator, and is generally also called a “source,” i.e., a source of the sound waves that are transmitted and then reflected/refracted off the ocean floor and then received by one or more, usually dozens, of receivers. Marine vibrators (herein after referred to as “vibrators,” “marine vibrators,” and/or “seismic vibrators”) can be implemented in what are referred to as “towed arrays” of the plurality of sources and their receivers, wherein each towed array can include numerous vibrators, numerous receivers, and can include several or more groups of receivers, each on its own cables, with a corresponding source, again on its own cable. Systems and methods for their use have been produced for devices that can maintain these cables, for example, in relatively straight lines as they are being towed behind ships in the ocean. As those of ordinary skill in the art can appreciate, an entire industry has been created to explore the oceans for new deposits of hydrocarbons, and has been referred to as “reflection seismology.”
For a seismic gathering process, as shown in FIG. 1, a data acquisition system 10 includes a ship 2 towing plural streamers 6 that may extend over kilometers behind ship 2. Each of the streamers 6 can include one or more birds 13 that maintains streamer 6 in a known fixed position relative to other streamers 6, and the birds 13 are capable of moving streamer 6 as desired according to bi-directional communications birds 13 can receive from ship 2. One or more source arrays 4a,b may be also towed by ship 2 or another ship for generating seismic waves. Source arrays 4a,b can be placed either in front of or behind receivers 14 (shown in FIG. 2), or both behind and in front of receivers 14. The seismic waves generated by source arrays 4a,b propagate downward, reflect off of, and penetrate the seafloor, wherein the refracted waves eventually are reflected by one or more reflecting structures (not shown in FIG. 1) back to the surface (see FIG. 2, discussed below). The reflected seismic waves propagate upwardly and are detected by receivers 14 provided on streamers 6. This process is generally referred to as “shooting” a particular seafloor area, and the seafloor area can be referred to as a “cell,” and the underground area can be referred to as the “geographical area of interest” (GAI).
FIG. 2 illustrates a side view of the data acquisition system 10 of FIG. 1. Ship 2, located on ocean surface 46, tows one or more streamers 6, that is comprised of cables 12, and a plurality of receivers 14. Shown in FIG. 2 are two source streamers, which include sources 4a,b attached to respective cables 12a,b. Each source 4a,b is capable of transmitting a respective sound wave, or transmitted signal 20a,b. For the sake of simplifying the discussion, but while not detracting at all from an understanding of the principles involved, only a first transmitted signal 20a will be discussed (even though some or all of source 4 can be simultaneously (or not) transmitting similar transmitted signals 20). First transmitted signal 20a travels through ocean 40 (note that ocean 40 need not necessarily be a saltwater body of water; it can also be a freshwater or brackish body of water) and arrives at first refraction/reflection point 22a. First reflected signal 24a from first transmitted signal 20a travels upward from ocean floor 42, back to receivers 14. As those of skill in the art can appreciate, whenever a signal—optical or acoustical—travels from one medium with a first index of refraction n1 and meets with a different medium, with a second index of refraction n2, a portion of the transmitted signal is reflected at an angle equal to the incident angle (according to the well-known Snell's law), and a second portion of the transmitted signal can be refracted (again according to Snell's law).
Thus, as shown in FIG. 2, first transmitted signal 20a generates first reflected signal 24a, and first refracted signal 26a. First refracted signal 26a travels through sediment layer 16 (which can be generically referred to as first subsurface layer 16) beneath ocean floor 42, and can now be considered to be a “new” transmitted signal, such that when it encounters a second medium at second refraction/reflection point 28a, a second set of refracted and reflected signals 32a and 30a, are subsequently generated. Further, as shown in FIG. 2, there happens to be a significant hydrocarbon deposit 44 within a third medium, or solid earth/rock layer 18 (which can be generically referred to as second subsurface layer 18). Consequently, refracted and reflected signals are generated by the hydrocarbon deposit, and it one of at least several purposes of data acquisition system 10 to generate data that can be used to discover such hydrocarbon deposits 44.
The signals recorded by seismic receivers 14 vary in time, having energy peaks that may correspond to reflectors between layers. In reality, since the sea floor and the air/water are highly reflective, some of the peaks correspond to multiple reflections or spurious reflections that should be eliminated before the geophysical structure can be correctly imaged. Primary waves suffer only one reflection from an interface between layers of the subsurface (e.g., first reflected signal 24a). Waves other than primary waves are known as multiples. As known by those of ordinary skill in the art, multiples can be generated in several different ways.
Velocity models are key components of seismic imaging, and consequently, to reservoir description and geo-mechanical analysis. As its name implies, a velocity model is a visual representation of the velocity of sound waves in different locations underground. Note that “underground” can mean in land-based areas, for example, within the continental United States, or underground under the ocean floor (but can also include the different velocities of the sound as it passed through different ocean water layers). Thus, as shown in FIG. 3, first sound wave 20a can have many different velocities as it travels from source 4a, through different water layers 41a-d, through different underground layers 16a-c, and is finally reflected and received by receivers (not shown in FIG. 3). As those of ordinary skill in the art can appreciate, in standard sea water conditions, the first velocity is in the order of about 1,500 meters-per-second (mps). FIG. 3, a greatly oversimplified view of a velocity model for a fictitious area, shows up to seven different velocity-constant layers. As shown, the layers are generally not flat, as shown in FIG. 4, which is an illustrative cross section of an actual thrust belt. A thrust belt is a geological formation caused by compressional tectonics, a natural process that ultimately results in the formation of large mountain ranges. As those of ordinary skill in the art can appreciate, thrust belts present both significant financial rewards as well as financial risk: significant oil and gas deposits can be found around thrust belts, but, not every thrust belt will exhibit the properties of oil and gas deposits, and so “bust” drillings can occur, at the cost of about ten million dollars or so per drilling.
If the sub-strata were more or less homogenous, the velocity model would be relatively easy to create (as shown, for example, in FIG. 3); however, it is known that there are many different geological factors that will make it very difficult to create accurate depictions of the velocity model. For example, some sub-surface areas have significant complex features such as strong velocity or anisotropic parameter variations or complex geological formations such as salt and basalt structures, heavily faulted zones, anisotropic environments due to sedimentation or fracturing (an anisotropic environment is one in which seismic waves move at higher or lower velocities depending upon whether they move in directions along or across rock bed layers), over-thrusts, shallow gas, among others. The processing of the reflected and refracted sound waves, therefore, can become extremely complicated.
Those of ordinary skill in the art can appreciate that velocity can vary depending upon such things as lithology (the type of rock), and depth of burial, since rocks under pressure tend to have higher velocity. Further, it is common to use colors, or shading, to represent a rainbow scale of rock velocity. Thus, similarly colored areas exhibit similar velocities. According to one non-limiting example, a first color or colors—purples and/or blues—represent the lower velocities in the range of 3,000 to 3,500 meters per second. A third set of colors—reds, yellows and oranges—represent velocities that are about 6,000 meters per second. A second set of colors, for example green, represents velocities that are in the range of about 4,000-5,000 meters per second. As discussed above, seismic data is obtained by generating sound waves, and locating receivers, usually a large number of them (in the order of several hundred to several thousand depending on the location and the expected underground geological topology), to collect the data.
Full waveform inversion (FWI) has been an important method to build velocity models for seismic imaging (see, Tarantola, A., 1984, “Inversion of Seismic Reflection Data in the Acoustic Approximation: Geophysics,” 49, 1259-1266; and Sirgue, L., and R. G. Pratt, 2004, “Efficient Waveform Inversion and Imaging: A strategy for Selecting Temporal Frequencies,” Geophysics, 69, 231-248; and Virieux, J., and S. Operto, 2009, “An Overview of Full Waveform Inversion in Exploration Geophysics,” Geophysics, 74(6), WCC127-WCC152, the entire contents of each of which are incorporated herein in their entirety). Classical FWI involves the minimization of a square misfit function between the calculated and observed data. Non-linear gradient based optimizations have also been used (see, Pratt, R., C. et al., 1998, “Gauss-Newton and Full Newton Methods in Frequency-Space Seismic Waveform Inversion,” Geophysical Journal, International, 13, p. 341-362; Ravaut, C. et al., 2004, “Multi-scale Imaging of Complex Structures from Multifold Wide-Aperture Seismic Data by Frequency-Domain Full Waveform Tomography Application to a Thrust Belt,” Geophysical Journal, International, 159, 3, p. 1032-1056; Sirgue, L., and R. G. Pratt, 2004, “Efficient waveform inversion and imaging: A Strategy for Selecting Temporal Frequencies,” Geophysics, 69, 231-248; Choi et al., 2008 “Frequency-Domain Full Waveform Inversions Using the new Pseudo-Hessian Matrix: Experience of Elastic Marmuosi-2 Synthetic Data.” Bulletin of the Seismological Society of America, 98, 2402-2415; Ma Y., et al., 2011, “A Projected Hessian Matrix for Full Waveform Inversion,” SEG, Expanded Abstracts, 30, 1, 2401-2405, the entire contents of each of which are incorporated herein in their entirety) with complex strategies for making the results more linear (filtering, weighting, and muting of the data, among other data manipulations). These strategies mitigate non-linearity but cannot recover the features that are not covered by the intrinsic resolution of the method.
The resolution of FWI is the resolution of a migration operator. The recovered wavelengths in the velocity model correspond to the time recorded wavelengths stretched to depth according to the local velocity and angular aperture. For the transmissions and refractions, the stretching due to the angle aperture allows recovery of the long wavelengths of the velocity model (see, Gauthier, O. et al, 1986, “Two-Dimensional Nonlinear Inversion of Seismic Waveforms: Numerical Results,” Geophysics, 51, no. 7, p. 1387-1403, the entire contents of which are incorporated herein by reference), while for the reflections, only short wavelengths can be recovered by FWI due to the narrow range of reflection angle apertures. This explains why FWI recovers long wavelength components of the velocity model only in shallow areas and why its resolution improves when lower frequencies and longer offset data are available (see, Ravaut, C. et al., 2004, “Multiscale Imaging of Complex Structures from Multifold Wide-Aperture Seismic Data by Frequency-Domain Full Waveform Tomography: Application to a Thrust Belt” Geophysical Journal, International, 159, 3, p. 1032-1056, and Sirgue, L., et al., 2010, “Full-Waveform Inversion: The Next Leap Forward in Imaging at Valhall: First Break,” 28, 65-70, the entire contents of all of which are incorporated herein by reference). Unfortunately for conventional streamer data, low frequencies are not available due to the existence of source and receiver ghosts (see, Lindsey, J. P., 1960, “Elimination of Seismic Ghost Reflections by Means of a Linear Filter,” Geophysics, 25, 1, p. 130-140, the entire contents of which are incorporated herein by reference), and the maximum offset is usually limited to within about 8 km.
The aforementioned problems mean that it remains a challenge in the application of FWI to streamer data to obtain good velocity resolution. These problems have been discussed in Plessix, R. E. et al, 2010, “Application of Acoustic Full Waveform Inversion to a Low-Frequency Large-Offset Land Data Set,” SEG, Expanded Abstracts, 29, 1, p. 930-934, the entire contents of which are incorporated herein by reference. Accordingly, it would be desirable to provide methods, modes and systems for improving the application of FWI to streamer data to obtain better velocity resolution.